I've been working my way through an introduction to Bayesian Inference in a Statistical Physics textbook (Tobochnik and Gould, 2010 - available online, excellent book). I've run across a problem that I can't quite wrap my head around, though I believed I understood Bayesian Inference up to that point (just before this was an amazing explanation of the Monty Hall problem using Bayes' Theorem).
What is happening here? I thought the chance of the test being right was 98%? Why would Bayes Theorem tell us that the chance of you actually having the disease given the positive result is less than 1 percent? What does that mean we're saying when we say that the test is 98% accurate? Does it have something to do with the fact that the disease is so rare?